mlsanityData to 7 Oct 2026

Scalable Inference in SDEs by Direct Matching of the Fokker-Planck-Kolmogorov Equation

arXiv 2110.15739 ↗First posted 29 Oct 2021cs.LG stat.MLcited by 14

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Abstract (arXiv)

Simulation-based techniques such as variants of stochastic Runge-Kutta are the de facto approach for inference with stochastic differential equations (SDEs) in machine learning. These methods are general-purpose and used with parametric and non-parametric models, and neural SDEs. Stochastic Runge-Kutta relies on the use of sampling schemes that can be inefficient in high dimensions. We address this issue by revisiting the classical SDE literature and derive direct approximations to the (typically intractable) Fokker-Planck-Kolmogorov equation by matching moments. We show how this workflow is fast, scales to high-dimensional latent spaces, and is applicable to scarce-data applications, where a non-parametric SDE with a driving Gaussian process velocity field specifies the model.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 20 of its 53 references that are in the map. First posted on arXiv 29 Oct 2021.

Builds on

20 of 53 references.

References · 20

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  6. 2018Neural Ordinary Differential Equationscited by 3,733
  7. 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 501
  8. 2020Scalable Gradients for Stochastic Differential Equationscited by 264
  9. 2014Scalable Variational Gaussian Process Classificationcited by 226
  10. 2019Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limitcited by 168
  11. 2021Neural SDEs as Infinite-Dimensional GANscited by 159
  12. 2016GPflow: A Gaussian process library using TensorFlowcited by 139
8 more
  1. 2018Gaussian Process Prior Variational Autoencoderscited by 72
  2. 2018Learning unknown ODE models with Gaussian processescited by 54
  3. 2014Variational Gaussian Process State-Space Modelscited by 43
  4. 2019ODE2VAE: Deep generative second order ODEs with Bayesian neural networkscited by 36
  5. 2018Learning Stochastic Differential Equations With Gaussian Processes Without Gradient Matchingcited by 23
  6. 2015Deep Temporal Sigmoid Belief Networks for Sequence Modelingcited by 13
  7. 2018Deep learning with differential Gaussian process flowscited by 11
  8. 2018Adaptive Path-Integral Autoencoder: Representation Learning and Planning for Dynamical Systemscited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 5; 2024: 4; 2025: 2; 2026: 1.

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  1. 2023Neural Continuous-Discrete State Space Models for Irregularly-Sampled Time Seriescited by 28
  2. 2022Self-Consistency of the Fokker-Planck Equationcited by 18
  3. 2023Modulated Neural ODEscited by 10
  4. 2024DynGMA: a robust approach for learning stochastic differential equations from datacited by 8
  5. 2023Bayesian Gaussian Process ODEs via Double Normalizing Flowscited by 7
  6. 2022Learning Interacting Dynamical Systems with Latent Gaussian Process ODEscited by 5
  7. 2023Cheap and Deterministic Inference for Deep State-Space Models of Interacting Dynamical Systemscited by 5
  8. 2024Fully Bayesian Differential Gaussian Processes through Stochastic Differential Equationscited by 4
  9. 2024Latent Space Energy-based Neural ODEscited by 4
  10. 2026Foundation Inference Models for Ordinary Differential Equationscited by 3
  11. 2023Sampling-Free Probabilistic Deep State-Space Modelscited by 2
  12. 2025Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutionscited by 2
2 more
  1. 2025Learning Stochastic Hamiltonian Systems via Stochastic Generating Function Neural Networkcited by 1
  2. 2024Learning to Approximate Particle Smoothing Trajectories via Diffusion Generative Modelscited by 0